Stealth chaos due to frame-dragging

Abstract

While the geodesic motion around a Kerr black hole is fully integrable and therefore regular, numerical explorations of the phase-space around other spacetime configurations, with a different multipolar structure, have displayed chaotic features. In most of these solutions, the role of the purely general relativistic effect of frame-dragging in chaos has eluded a definite answer. In this work, we show that, when considering neutral test particles around a family of stationary axially-symmetric analytical exact solution to the Einstein–Maxwell field equations, frame-dragging (as captured through spacetime vorticity) is capable of reconstructing KAM-tori from initially highly chaotic configurations. We study this reconstruction by isolating the contribution of the spacetime vorticity scalar to the dynamics, and exemplify our findings by computing rotation curves and the dimensionality of phase-space. Since signatures of chaotic dynamics in gravitational waves have been suggested as a way to test general relativity in the strong-field regime, we have computed gravitational waveforms using the semi-relativistic approximation and studied the frequency content of the gravitational wave spectrum. If this mechanism is generic, chaos suppression by frame-dragging may undermine present proposals to verify the hypothesis of the no-hair theorems and the validity of general relativity.

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

“…A gravitomagnetic origin of friction for black-hole dynamics was investigated by Cashen et al [94], while Gutiérrez-Ruiz et al [95] focused on the possible impact of frame-dragging on chaotic dynamics of test particles around a family of stationary axially-symmetric solutions of Einstein's equation coupled with electromagnetic fields. The Aharonov-Bohm effect for the gravitational field of rotating cosmic string was studied by Barros et al [96].…”

Minimal length effects on motion of a particle in Rindler space *

“…In a universal way, the particle chaotic motion has lately been studied near the black hole horizon [12][13][14]. Interestingly, gravitational waves emitted from chaotic motions of particles in a bumpy spacetime can be used to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr background spacetime [15]. Recently, it has been shown that such a proposal may be undermined due to chaos suppression by frame dragging [16].…”